Copula-Based Regression with Mixed Covariates

Saeed Aldahmani, Othmane Kortbi () and Mhamed Mesfioui
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Saeed Aldahmani: Department of Statistics and Business Analytics, UAE University, Al Ain P.O. Box 15551, United Arab Emirates
Othmane Kortbi: Department of Statistics and Business Analytics, UAE University, Al Ain P.O. Box 15551, United Arab Emirates
Mhamed Mesfioui: Département de Mathématiques et d’Informatique, Université du Québec à Trois-Rivières, Trois-Rivières, QC G9A 5H7, Canada

Mathematics, 2024, vol. 12, issue 22, 1-15

Abstract: In this paper, we focused on developing copula-based modeling procedures that effectively capture the dependence between response and explanatory variables. Building upon the work of Noh et al. (J. Am. Stat. Assoc. 2013, 108, 676–688) we extended copula-based regression to accommodate both continuous and discrete covariates. Specifically, we explored the construction of copulas to estimate the conditional mean of the response variable given the covariates, elucidating the relationship between copula structures and marginal distributions. We considered various estimation methods for copulas and distribution functions, presenting a diverse array of estimators for the conditional mean function. These estimators range from non-parametric to semi-parametric and fully parametric, offering flexibility in modeling regression relationships. An adapted algorithm is applied to construct copulas and simulations are carried out to replicate datasets, estimate prediction model parameters, and compare with the OLS method. The practicality and efficacy of our proposed methodologies, grounded in the principles of copula-based regression, are substantiated through methodical simulation studies.

Keywords: least squares regression; copulas; copula-based regression; archimedean copulas; gaussian copula; IMSE (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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